Fractional order system of integro-differential equations: theoretical and numerical simulations using Appell-type Changhee polynomials

Volume 34, Issue 1, pp 74--84 https://dx.doi.org/10.22436/jmcs.034.01.07

Publication Date: February 23, 2024 Submission Date: December 11, 2023 Revision Date: December 22, 2023 Accteptance Date: January 15, 2024

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Authors

M. Adel - Department of Mathematics, Faculty of Science, Islamic University of Madinah, Medina 42210, KSA. - Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt.

Abstract

We examine the behavior of the solutions for a fractional-order integro-differential equation (FIDE) system using an efficient simulation presented in this paper. The FIDEs are treated by a presumably novel approximation method based on Changhee polynomials of Appell type (ACPs). In this work, we use the method of spectral collocation (SCM), which is based on the advantages of ACPs. Using this technique on the given model, it generates an algebraic equation system. Through the evaluation of the residual error function (REF), we verify the efficiency of the approach that has been offered. To verify the effectiveness and originality of the suggested algorithm, the results are compared with the precise solutions. Our results show that the method employed provides a straightforward and efficient tool to simulate the solution for such models. The suggested method's primary benefits are that it only requires a few easy steps and doesn't generate secular terms.

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Keywords

• Fractional integro-differential equations
• Liouville-Caputo fractional derivative
• ACPs
• SCM

MSC

•  34A12
•  41A30
•  47H10
•  65N20

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